Modified dynamical systems retain Turing universality.
problem Embedding Turing machines into dynamical systems.
method Exploring flows with adapted 1-forms and homogeneity.
result Even slight modifications can lead to Turing universality.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
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48 results for “Flow Dynamics”
Study on stability of hyperkähler flow in 4-manifolds.
problem Stability of hyperkähler flow in 4-manifolds.
method Extending results from mean curvature flow for minimal surfaces to hyperkähler flow.
result Obtained a dynamic stability theorem for hyperkähler flow.
Study stability and instability of Ricci-flat metrics under generalized Ricci flow.
problem Stability and instability of Ricci-flat metrics under Ricci flow.
method Analysis of generalized Ricci flow for Ricci-flat metrics and vanishing 3-forms.
result Dynamical stability and instability results for Ricci-flat metrics and vanishing 3-forms.
Paper defines dynamical coherence for flows and proves it under specific conditions.
problem Understanding the dynamics of partially hyperbolic flows.
method Introduces dynamical coherence and proves it for flows with a specific foliation.
result Dynamical coherence proved for flows with a particular foliation.
Identifies most probable flows for Kunita SDEs in fluid dynamics.
problem Modeling stochastic processes with Eulerian noise and deterministic drifts.
method Equipping the domain with a Riemannian metric from the noise, solving the resulting PDEs.
result Most probable flows differ from deterministic flows, especially under noise.
The study examines stability of specific geometric flows.
problem Stability of Pluriclosed and Generalized Ricci solitons.
method Analyzes the second variation of generalized Einstein--Hilbert functional and infinitesimal deformations.
result Stability of the flows and solitons under specific conditions.
New energy functional bounds Ricci flows on ancient spaces.
problem Bounding Ricci flows on ancient spaces.
method Introducing a dynamical energy functional on compact ancient asymptotically Ricci-flat Ricci flows.
result Provides an upper bound for the ordinary λ-functional.
Paper studies generic dynamics of MCFs with spherical singularities.
problem Characterizing the generic behavior of mean curvature flow with spherical singularities.
method Level set formulation of mean curvature flow, analysis of arrival time function.
result Generically, the arrival time function has at most regularity.
New method learns population dynamics from snapshots, outperforming existing models.
problem Capturing periodic and other dynamical properties of population dynamics.
method Wasserstein Lagrangian Mechanics (WLM) for learning second-order dynamics from observed marginals.
result WLM outperforms existing methods across various dynamics, including vortex dynamics, embryonic development, and flocking.
New method learns flows between multiple distributions efficiently.
problem Learning dynamic transport maps between multiple empirical distributions.
method Combining flow matching and dynamic optimal transport with potential terms.
result OTP-FM achieves state-of-the-art performance on various datasets.
Study dynamics and topology of flows near non-saddle sets or W-sets.
problem Understanding the dynamics and topology of flows near specific invariant sets.
method Cohomological relations and global properties analysis.
result Dynamical classification of surfaces and robustness of non-saddle-sets.
It is known that the Langevin dynamics used in MCMC is the gradient flow of the KL divergence on the Wasserstein space, which helps convergence analysis and inspires recent particle-based variational inference methods (ParVIs). But no more MCMC dynamics is understood in this way. In this work, by developing novel conce…
Paper introduces Tensor Gauge Flow Models for better data encoding.
problem Lack of expressive flow dynamics in existing Generative Flow Models.
method Incorporates higher-order Tensor Gauge Fields into the Flow Equation.
result Tensor Gauge Flow Models achieve improved generative performance.
Study connects flow dynamics to 3D geometry via surface intersections.
problem Relating flow dynamics to geometric properties of 3-manifolds.
method Relates pseudo-Anosov flow dynamics to hyperbolic geometry via curve graphs.
result Established a link between flow invariants and geometric features of 3-manifolds.
Study of mean curvature flows with conical singularities using mathematical techniques.
problem Understanding the dynamics of mean curvature flows near conical singularities.
method Feynman-Kac formula and invariant cone method for noncompact settings.
result Generic initial perturbations avoid conical singularities in mean curvature flows.
Mutations and faces of the Thurston norm ball dynamically represented by multiple distinct flowsmath.GT
New flows represent Thurston norm ball faces, differing by veering mutations.
problem Dynamic representation of Thurston norm ball faces by distinct flows.
method Combining veering triangulations and mutations to represent faces by multiple flows.
result Non-fibered faces can be represented by two distinct flows differing by veering mutations.
The Ricci flow is a parabolic evolution equation in the space of Riemannian metrics of a smooth manifold. To some extent, Einstein equations give rise to a similar hyperbolic evolution. The present text is an introductory exposition to Bianchi-Ricci and Bianchi-Einstein flows, that is, the restricted finitely dimension…
Sparse Kernel Flows learns dynamical systems from data.
problem Learning dynamical systems from limited data.
method Sparse Kernel Flows: trains optimal kernel from a dictionary of kernels.
result Sparse Kernel Flows can learn from 132 chaotic systems.
sFML learns stochastic dynamical systems from data.
problem Learning unknown stochastic dynamical systems from measurement data.
method sFML extends FML for deterministic systems, using a stochastic flow map composed of deterministic and stochastic sub-maps.
result sFML constructs a stochastic evolution model approximating unknown stochastic systems.
Symbolic dynamics for flows in high dimensions, extending previous work.
problem Coding flows with positive speed in high dimensions.
method Construct symbolic dynamics for flows with positive speed in any dimension.
result Extended symbolic dynamics to flows in high dimensions, including homoclinic classes.
Stability of Type IIA flow ensures Kähler properties of Calabi-Yau 3-folds.
problem Ensuring the Kähler property of Calabi-Yau 3-folds under symplectic deformations.
method Established dynamical stability of Type IIA flow near stationary points.
result Stability of Type IIA flow ensures the stability of Kähler properties under symplectic deformations.
Continuity of earthquake flow map transfers Teichmüller dynamics results.
problem Transfer results from Teichmüller dynamics to earthquake flow.
method Analyze continuity of earthquake flow map and its inverse.
result Transfer results from Teichmüller dynamics to earthquake flow.
This study explains gradient flow dynamics in neural networks for small initialisation.
problem Understanding the training dynamics of neural networks for small initialisation.
method Analysis of gradient flow dynamics for one-hidden layer ReLU networks with orthogonal inputs.
result Gradient flow converges to zero loss and characterizes implicit bias towards minimum variation norm.
Method learns PDE dynamics via evolving latent manifold using Ricci flow.
problem Learning dynamics in time, especially PDEs, with low-dimensional representations.
method Parameterizes latent manifold, simulates Ricci flow physics-informedly, matching manifold quantities.
result Ricci flow facilitates learning for out-of-distribution data and adversarial robustness.
Parabolic geometric flows have the property of smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of this paper is that, by bringing in the dynamical properties of the flow, we obtain also smoothing for long time for g…
Study on Ricci flows of awesome homogeneous spaces, proving finite extinction time.
problem Understanding the long-time behavior of Ricci flows on homogeneous spaces.
method Analyzing Ricci flows on non-compact manifolds, focusing on finite extinction time.
result Ricci flows on non-contractible spaces have finite extinction time, confirming conjecture.
This paper explains how predictable order flow can lead to Brownian motion in financial prices.
problem Why financial prices exhibit Brownian motion despite predictable order flow.
method Generalized Lillo-Mike-Farmer model to nonlinear price-impact dynamics, mapping to Lévy-walk model.
result Price dynamics remain diffusive under the square-root law, even with persistent order flow.
Study shows how macroeconomic news affects intraday price and order flow dynamics.
problem Understanding how macroeconomic news impacts intraday price and order flow dynamics.
method Structural VAR model identified through heteroskedasticity, estimated at one-second frequency for each 15-minute interval.
result Macroeconomic news announcements reshape price-flow dynamics, with significant impacts on price and flow impacts at the one-second horizon.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
Study perturbs mean curvature flow near non-spherical shrinkers.
problem Understanding the dynamics near non-spherical shrinkers under mean curvature flow.
method Invariant manifold theory from hyperbolic dynamics.
result Generic perturbation makes flow leave a neighborhood of non-spherical shrinkers.
RC flow learns molecular kinetics in low dimensions.
problem Discovering interpretable low-dimensional models of molecular kinetics.
method Normalizing flow for coordinate transformation and Brownian dynamics for kinetics approximation.
result Tractable and trainable model of reduced kinetics in continuous time and space.
Study on test risk dynamics in learning theory with stochastic gradient flow.
problem Understanding test risk in stochastic gradient flow dynamics.
method Path integral formulation for small learning rates, explicit computation for weak features.
result Explicit corrections due to stochastic term in dynamics, good agreement with simulations.
Study non-Weinstein Liouville geometry via hyperbolic dynamics, proving rigidity results.
problem Characterize non-Weinstein Liouville geometry with persistent transverse skeleton.
method Anosov 3-flows, Liouville Interpolation Systems, non-singular partially hyperbolic flows, hyperbolic dynamics.
result Mitsumatsu's examples characterize 4D non-Weinstein Liouville geometry with 3D persistent transverse skeleton.
Invites study of contact structures and Reeb flows dynamics.
problem Relating dynamics of two Reeb flows of the same contact structure.
method Gathers results and poses many questions and conjectures.
result Many new questions and conjectures posed.
The study characterizes straight-line flows in dynamic measure transport.
problem Tackles the challenge of designing flows that are easy to integrate.
method Characterizes straight-line flows using a PDE and Reynolds tensor.
result Characterizes affine-in-time interpolants and necessary conditions for flow geometry.
New dynamics for SGD in small learning rate regime.
problem Improving stochastic gradient descent in small learning rate regime.
method Introducing stochastic modified flows and distribution dependent stochastic modified flows.
result Captures fluctuating dynamics of SGD in small learning rate - infinite width scaling regime.
Characterizes Anosov flows via contact geometry.
problem Understanding Anosov 3-flows through contact geometry.
method Investigates interactions with Reeb dynamics and proves a technical theorem.
result Space of adapted geometries homotopy equivalent to Anosov flows.
Anosov flow found in specific partially hyperbolic systems.
problem Characterizing partially hyperbolic diffeomorphisms with center foliation.
method Analyzing transitive dynamically coherent systems with one-dimensional center foliation.
result Discretized Anosov flow found in systems satisfying for center leaves.
Study shows partial hyperbolicity leads to Anosov dynamics in 3-manifolds.
problem Understanding dynamics in hyperbolic 3-manifolds and Seifert manifolds.
method Classification of partially hyperbolic diffeomorphisms and pseudo-Anosov dynamics.
result Complete classification of partially hyperbolic diffeomorphisms in hyperbolic 3-manifolds and Seifert manifolds.
Heisenberg Translation Flowsmath.DS
Study of flows on circle bundles over translation surfaces, showing decay of correlations.
problem Ergodic properties of flows on circle bundles over translation surfaces.
method Generalizing Heisenberg nilflows to more general base surfaces, showing relatively mixing.
result Showed that such flows exhibit decay of correlations in the orthogonal complement of functions constant along fibers.
Proved dynamical Alekseevskii conjecture in 5D.
problem Proving the Alekseevskii conjecture in 5D.
method Detailed analysis of homogeneous Ricci flows.
result Proved the dynamical Alekseevskii conjecture in 5D.
Stochastic Price Dynamics in Response to Order Flow Imbalance: Evidence from CSI 300 Index Futuresq-fin.MF
Modeling price dynamics in response to order flow imbalance in Chinese futures markets.
problem Understanding price dynamics in markets with order flow imbalance.
method Modeling order flow imbalance as an Ornstein-Uhlenbeck process with memory and mean-reverting characteristics.
result Horizon-dependent heterogeneity in conventional metrics' interaction with order flow imbalance.
Noncompact Ricci-flat solutions have infinite unstable dimensions.
problem Understanding unstable dimensions of noncompact Ricci-flat solutions.
method Derived sufficient conditions for infinite-dimensional unstable manifolds.
result Noncompact Ricci-flat solutions have uncountably many unstable perturbations.
The radial Newton problem: nonlinear dynamics of minimal resistance in central fieldsphysics.flu-dyn
The paper studies minimal resistance dynamics in radial fields, finding unique solutions for incompressible flows.
problem Nonlinear dynamics of minimal resistance in radial fields.
method Analysis of two non-equilibrium scenarios: scale-invariant free expansion and incompressible source flow.
result Incompressible flow acts as a structural regularizer, admitting unique, smooth, and strictly concave solutions.
The paper analyzes neural network dynamics after weights escape the origin.
problem Understanding gradient flow dynamics of neural networks after the origin.
method Analyzes gradient flow of homogeneous neural networks with locally Lipschitz gradients.
result Characterizes the first saddle point encountered after escaping the origin.
The paper models star dynamics using Ricci flow and Perelman entropy, revealing chaotic behavior.
problem Modeling chaotic positional dynamics of stars in celestial systems.
method Discrete dynamical systems, Ricci flow, Perelman entropy, Lyapunov exponents, bifurcation analysis.
result Entropy increases exponentially, indicating challenging long-term star position prediction.
Paper connects knot invariants and Morse flow loops.
problem Connecting quantum group invariants and Morse flow loops for knot study.
method Defining a two-variable series invariant by counting Morse flow loops in knot complements and proving it agrees with quantum group BPS series.
result Correspondence proven for all braid-homogeneous knots.
The execution flow drives market dynamics, validated on real data.
problem Understanding the fundamental driving force of market dynamics.
method Developed a numerical framework using the Radon-Nikodym derivative to calculate execution flow and determined thresholds and characteristic time scales.
result Execution flow is the fundamental driving force of market dynamics.